Geometric Quantum Computation
We present a new model of quantum computation rooted in the representation theory of the mass less sector of unitary irreducible representations of the extended Poincare group developed in [1].
quant-ph↗
arXiv subjects
Marco Zaopo
Publications and source records attributed to Marco Zaopo.
Group Representations of Lorentz Transformations Extended to Superluminal Observers
We construct an extension of the proper orthochronous Lorentz group that includes space-time transformations for observers moving with superluminal relative velocities in arbitrary direction. This extension is generated by a realization of the Klein four group depending on polar and azimuthal angles identifying a spatial direction and is obtained with matrices representing infinite velocity limits of superluminal Lorentz boosts. The resulting group has the same identity component of the whole Lorentz group O(3,1) but involutive operators corresponding to an infinite speed boost and its negative in place of parity and time reversal. Different spatial directions in the definition of Klein group realization give rise to equivalent group extensions. We then define the extended Poincare group including translations and classify its unitary irreducible representations (UIRs). The resulting UIRs are induced from Wigner's UIRs of standard Poincare group and depend on the action of the extended Lorentz group defined on momentum space. UIRs corresponding to non lightlike orbits restrict to the ordinary Poincare subgroup as a multiplicity one direct sum of a massive forward, a massive backward and a tachyonic Wigner UIR while for lightlike orbits as two inequivalent direct sum representations combiningh linearly a forward and backward massless Wigner UIR. We then derive wave equations corresponding to solutions of the Casimir eigenvalue problem of Poincare algebra obtained differentiating the above representations. This set of equations contains all the wave equations known to date in quantum field theory together with new wave equations describing tachyonic behaviour and a new class of massless representations. We finally show that tachyonic wave functions provide a relevant representation theoretic tool for interpretation of parity violation phenomena in quantum field theory
hep-th↗
Principle of relativity for quantum theory
In non relativistic physics it is assumed that both chronological ordering and causal ordering of events (telling whether there exists a causal relationship between two events or not) are absolute, observer independent properties. In relativistic physics on the other hand chronological ordering depends on the observer who assigns space-time coordinates to physical events and only causal ordering is regarded as an observer independent property. In this paper it is shown that quantum theory can be considered as a physical theory in which causal (as well as chronological) ordering of probabilistic events happening in experiments may be regarded as an observer dependent property.
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Information Theoretic Axioms for Quantum Theory
In this paper we derive the complex Hilbert space formalism of quantum theory from four simple information theoretic axioms. It is shown that quantum theory is the only non classical probabilistic theory satisfying the following axioms: distinguishability, conservation, reversibility, composition. The new results of this reconstruction compared to other reconstructions by other authors are: (i) we get rid of axiom "subspace" in favor of axiom conservation eliminating mathematical requirements contained in previous axiomatics; (ii) we are able to classify all the probabilistic theories that are consistent requiring (a) only the first two axioms (b) only the first three axioms; this could be useful in experimental tests of quantum theory since it gives the possibility to understand whether or not other mathematical models could be consistent with such tests; (iii) we provide a connection between two different approaches to quantum foundations, quantum logic and the one based on information theoretic primitives showing that any theory satisfying the first two axioms given above either is classical or is a theory in which physical systems are described by a projective geometry.
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Relativity of Causal Structure in Quantum Theory
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in the region of space where is situated a physical device has a certain value of a physical observable at the time when the device fires the outcome corresponding to that value of the observable. The causal structure of these events is customarily assumed fixed in an absolute way. In this paper we show that this assumption cannot be substantiated on operational grounds proving that two observers looking at the same quantum experiment can calculate the probabilities of the experiment assuming a different causal structure for the space-time events constituted by the outcomes. We will thus say that in quantum theory we have relativity of causal structure.
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